I agree with your conclusion, but I'm not sure about your argument. The key is dimensionality.
Intensional definitions are able to combine not just physical stuff, but conceptual features. You can use words to describe something to me whose physical building blocks are not in my ontology, so long as the conceptual building blocks are in my feature-space.
It's sort of like how neural nets can generalize outside of their training data by learning features and then describing new things in terms of those features.
The point is, if you observe something ontologically new, and you want to tell me about it, the process you use to tell me is identical to "relabeling" - you just combine mental features to describe the thing, and communicate it. Only the observation was special; you can't single out some type of communication as "only possible about new things" by nature of its syntax.
Your examples in this post (Gaia, Beauty), are two similar mistakes - assuming that since there's a label, it must be labeling something important, basic, and with the expected connotations.
Maybe the fact that these examples are similar is actually a bit of a reminder to look into the dark.
Anyhow, syntactically speaking, these are perfectly valid external references. You say:
For example, we might only be able to define how quarks interact with each other but not say what their nature actually is apart from being things that interact in that particular way (some might say that behaviour is all that there is to the nature of something, but then what's the difference between an atom and a simulation of an atom?). If this were the case, then we'd have to define them as an external reference.
(Huh, are you British? I was assuming you were American. Sorry if that's nosy.)
The Beauty-essentialist could just as easily claim that they are making an external reference.
"For example, we might only be able to define how Beauty interacts with our awareness, but not what its nature actually is apart from being a thing that interacts with us in a particular way." - David Chalmers, probably
Suppose we even want to ground ourselves directly with an extensional definition. You might point at an STM image of an electron orbital and say "there: that is an electron." What is stopping the beautician from pointing at the Venus de Milo and saying "there: that is beauty."?
So I don't see how your examples illustrate a relabeling vs. external reference distinction. What is wrong with them is not that they are "relabelings," is that we (reductionists) accept only a certain sort of complicated work as evidence that something is ontologically fundamental, and the beautician hasn't done that work, and is in fact contradicting other, more careful work.
Yes, you can posit that they are external references, my main point was that if they aren't external references but merely relabellings, then they don't change the system and so it's invalid to try to sneak in the connotations being attempted. Sometimes people try a motte and bailey where they say they are just making a definition and not positing something new; but then they act as though the thing they said was just a relabelling has its own existence.
So I don't see how your examples illustrate a relabeling vs. external reference distinction.
Part of what makes this so complex is that the same thing can be introduced as either a relabeling or an external reference. And people often do a half-and-half as I've described
The following distinction is crucial to my understanding of consciousness and epistemology. It is also extremely useful for seeing through some of the language games people play in terms of framing. There are fundamentally two ways in which we can define entities and much confusion is created by failing to distinguish between the two.
The first way is relabelling where we define something in terms of what we've already defined. If we've already defined the meaning of hydrogen atoms, oxygen atoms and molecules, then we can simply define water as a molecule consisting of one hydrogen atom and two oxygen atoms, if that's how we want to define it. Defining water in this way postulate a new entity in our fundamental ontology, but instead reuses existing elements.
The second way is to define an external reference; that is, a reference that doesn't purely build on top of already defined language or meaning. It is a very common belief that we can only define something in terms of things that have already been defined, but if that were the case, then we wouldn't even be able to get our first definition of the ground. All our definitions would either be circular or involve an infinite regress.
External references provide a not completely satisfactory, but pragmatically necessary workaround. Instead of being impractically purist when it comes to definitions, we allow ourselves to point to (or vaguely gesture at) things without being able to fully say what they are.
Let's imagine that quarks are the foundational element of physics as far as we can tell. Well, we could define quarks by how they interact with each other, but that is a surface level characteristic, which doesn't seem to explain what exactly they are at their fundamental core And if these quarks have a nature beyond their behaviour, then it makes sense to think about them as external references.
Some might say that the observable behaviour of these quarks is all that there is to their nature. If this is the case, then I would like to ask what is the difference between an atom and a simulation of an atom? Or even if I concede these quarks can be defined in terms of behaviour, what exactly is behaviour at its core? It doesn't seem like we can define behaviour in terms of behaviour and saying "It is what it is" seems like a way of obscuring that we don't know what it is. At the end of the day, it seems there has to be some deeper nature somewhere.
Here's another way of putting this: Relabeling defines a new entity in the map; external references posit a new entity in the territory (see: map and territory)
Relabelings don't change a system
Creating a relabeling doesn't affect reality (alternate phrasing: adding a new entity in the map doesn't change the territory). Here's an example: Let's suppose I introduce a new label "Gaia" and I say that by this I only mean the natural world and nothing more. Well, there's no reason why I can't use the word Gaia for this, however, most of the time people do this
I'm allowed to define terms however I want, however I shouldn't use this to trick you into accepting the connotations of the term, for example, that nature is some kind of divine being or provides a perfect order. I wouldn't object if someone argued that nature has these properties separately and chose to use the term to emphasise those aspects, but we shouldn't accept an argument by definition.
This is a Motte and Bailey argument. The Mott is the claim that they are just using a slightly unusual term for the natural world. The Bailey is that the natural world has the properties we tend to associate with this term. Or in my terminology, Gaia is a relabelling and it perhaps the framing might help us understand and talk about the system, but introducing it doesn't change anything. For any argument we can make using the term "Gaia", we should be able to make the same argument without it (see: Tabooing your words). Adding the relabelling "Gaia" into the system doesn't add divinity or a perfect order into the system. If they are present, they should still be present after we remove that relabelling.
Here's another example: a reasonable number of people believe that it is intrinsically valuable for beauty to exist in the world, even if no-one ever experiences it. "Intrinsically valuable" can mean different things to different people, but here let's take it to claim some kind of objective value independent of any observer. Similarly, I think most people wouldn't object to defining an object being beautiful as meaning that it meets certain aesthetic criteria when viewed by most humans.
I don't want to claim that the claim of intrinsic value is definitively false, but I believe we should be highly suspicious of this claim. The claim that beauty is intrinsically valuable seems to lean upon the conception of beauty as an intrinsic property of objects. Once we taboo the word beautiful, the argument becomes much less compelling. Beauty just seems a relabeling which matches particular combinations of atoms. It becomes natural to ask, "What is so special about these combinations that makes them valuable when other combinations are not?" And if the only thing that is special about these combinations is that they create a certain experience when viewed by a human, then this doesn't seem to provide a reason to think them valuable when not viewed by a human. Perhaps there is a way to justify this, but this isn't a sufficient argument by itself.
Next Steps
Ultimately, I'm trying to build up towards making a point about consciousness, which I know will be controversial since I tried making it here before and it met with significant opposition. I decided that it would be logical to take a step back and clarify my epistemological stance, in the hope that it might reduce the chance that we end up talking past each other.